Machine-guided Solution to Mathematical Word Problems

PACLIC 28 !111 Machine-Guided Solution to Mathematical Word Problems Bussaba Amnueypornsakul University of Illinois, Urbana-Champaign, USA amnueyp1@illinois.edu Suma Bhat University of Illinois Urbana-Champaign, USA spbhat2@illinois.edu Abstract Mathematical word problems (MWP) test crit- ical aspects of reading comprehension in con- junction with generating a solution that agrees with the “story” in the problem. In this paper we design and construct an MWP solver in a systematic manner, as a step towards enabling comprehension in mathematics and teaching problem solving for children in the elemen- tary grades. We do this by (a) identifying the discourse structure of MWPs that will enable comprehension in mathematics, and (b) utiliz- ing the information in the discourse structure towards generating the solution in a systematic manner. We build a multistage software proto- type that predicts the problem type, identifies the function of sentences in each problem, and extracts the necessary information from the question to generate the corresponding math- ematical equation. Our prototype has an ac- curacy of 86% on a large corpus of MWPs of three problem types from elementary grade mathematics curriculum. 1 Introduction Mathematical word problems (MWP) constitute an integral part of a child’s elementary schooling cur- riculum. Solving an MWP is a complex task in- volving critical aspects of reading comprehension (understanding the components of the problem), and generating a solution that agrees with the ‘story’ in the problem. Children are trained through the pro- cess of problem solving by the use of various strate- gies. In this study, we formulate solving an MWP as an NLP task involving text classification, discourse processing and information extraction. Our primary goal is to guide young learners through the impor- tant steps of mathematics comprehension and prob- lem solving of arithmetic word problems commonly encountered in the elementary grades. We take a bottom-up approach, identifying the discourse struc- ture of the MWP and then utilizing the semantic in- formation contained in the components of the prob- lem to generate a solution. In an MWP, significant background information is presented in text format. The ability to solve an MWP critically depends on the ability to detect the problem type and identify the components of the word problem as observed in studies in mathemat- ics education and cognitive psychology (De Corte and Verschaffel, 1987; Cummins, 1991; Verschaffel et al., 2000). Motivated by these studies, we divide the overall problem solving process into stages: predicting the problem type, identification of the function of sen- tences (or sentence type) in each problem, and ex- tracting the necessary information from the question to generate the corresponding mathematical equa- tion. Since classification of the problem and sen- tence types involves a decision based on the textual representation, the classification tasks can be viewed as automatic text categorization problems (Yang and Liu, 1999) with domain-specific feature engineer- ing. More broadly, a knowledge of the discourse structure of an MWP provides the human solver with a critical first step for information extraction and text summarization needed for mathematics problem comprehension and solving. A …

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